SAO PAULO She's one of the world's most popular presidents with an approval rating that is the envy of her peers in richer countries struggling with debt crises and political deadlock - 79 percent and rising.

She presides over a country with record-low unemployment, a can-do optimism that invites comparisons to the post-war years in the United States, and a chance to showcase its progress when it hosts the soccer World Cup next year.

And yet, it's entirely possible that Dilma Rousseff could fail to win re-election as president of Brazil in October 2014.

The 65-year-old leftist remains the clear favorite but the threat of rising inflation and unemployment, a trio of attractive opposition candidates, and the possibility of an embarrassing logistical debacle at the World Cup mean that Rousseff is less of a shoo-in than many observers think.

"It's probably going to be the most competitive election in Brazil in a decade," said João Augusto de Castro Neves, an analyst for the Eurasia Group think tank. "If you look, most of the ingredients for a tight race are in place."

The main ingredient is the economy.

In some ways, it's Rousseff's biggest strength. Unemployment was 5.6 percent in February, the lowest ever for that month. Real wages continue to rise, just as they have for most of the past decade as Brazil's economy enjoyed a historic boom, lifting some 35 million people - equivalent to the population of California - out of poverty.

That past and present success best explains why Rousseff's approval rating ticked up to 79 percent in a nationwide poll sponsored by industrial lobby group CNI last month. Sixty-three percent of respondents rated her government as good or very good.

If those numbers hold, Rousseff will be virtually impossible to beat. Castro Neves cited a study by polling group Ipsos that looked at more than 200 elections around the world over the past two decades, and found that leaders with an approval rating above 60 percent have a nine-in-10 chance of being re-elected.

Yet, not far beneath the surface, there are clear economic problems that could jump up and bite Rousseff, and erode those enviable ratings, just as her re-election bid gets underway.

HOW LONG CAN IT LAST?

The most likely villain - though not the most dangerous one - is inflation.

Prices rose 6.43 percent in the year through mid-March, and look set to creep even higher in coming months. Brazil's central bank said last week it sees a one-in-four chance that inflation could finish this year above its target ceiling of 6.5 percent - double the odds it saw three months before.

Brazilians are extremely sensitive to rising prices, mainly because of past horrors. Hyperinflation spiked over 2,500 percent just two decades ago, and people appreciate that the country's recent success was possible only because it got that problem under control.

Most voters aren't mad about rising prices yet, because wages have been rising even faster - by an average margin of about 3 percent last year. So, a tiny plurality in the CNI poll said they approved of Rousseff's handling of inflation, by a margin of 48 percent to 47 percent - a result that was a positive surprise to some in the presidential palace.

Can it last? To quote a member of Rousseff's economic team: "Anybody who tells you they know is lying."

That's because Brazil's economy is behaving strangely, and there's no manual for where it's headed. Solid wage growth has come even as gross domestic product grew just 2.7 percent in 2011 and 0.9 percent in 2012. Projections for 3 percent GDP growth this year are starting to look optimistic.

Rousseff's popularity proves that Brazilian voters do not care one whit about GDP. But business leaders do, and they're the ones who provide most of the jobs.

To that end, several gauges of business sentiment are looking shaky.

Brazil's stock market tumbled 7.55 percent from January to March, the worst first quarter in 18 years, at a time when markets in the United States were soaring to new highs. Industrial output fell 2.5 percent in February, its worst performance since the depths of the global financial crisis in late 2008, dashing hopes that Rousseff's numerous stimulus packages might have helped manufacturers turn the corner.

Consumer spending has been the economy's savior for years now, sustained by cheaper and more widely available credit. But high inflation means the central bank will probably have to start hiking interest rates as soon as May or June.

So the question boils down to this: Will Brazilian companies continue to create more jobs, and pay better wages, if the economy enters a third straight year of sluggish growth with no clear end in sight, at the same time as credit is becoming more expensive and consumption is starting to slow?

The answer could very well be yes: companies have so far continued to bet that Brazil's long-term future remains bright.

But if the answer is no, then inflation will become a bigger political issue, and the biggest hazard of all to Rousseff's re-election could emerge: rising unemployment. And then 2014 could turn into a very interesting election indeed.

EYES ON THE WORLD CUP

Another core truth about Rousseff is that, while she's widely respected and even admired, she is not beloved - at least not to the same extent as her predecessor Luiz Inacio Lula da Silva, who governed Brazil from 2003 to 2010.

A career government official who had never run for election before winning the presidency, and still sometimes looks strained speaking to crowds, Rousseff has built her image around the idea she is a sober steward of the economy.

The flip side of that: If the economy fades further, there's not a lot else to sustain her popularity.

In the CNI poll, she got her highest marks for fighting poverty, hunger and unemployment. But majorities disapproved of her handling of healthcare (67 percent), public safety (66 percent) and education (50 percent) - issues that are becoming higher priorities as more move into the middle class.

Similarly, the emphasis on administrative competence as Rousseff's primary job skill leaves her especially vulnerable to a snafu at the World Cup, which will be held just three months before the presidential election.

World soccer body FIFA has voiced concerns that stadiums won't be ready on time, and Brazil suffers terrible bottlenecks at airports, roads and public transport networks even on its best days.

A major logistical meltdown could be used by the opposition to undercut Rousseff's main perceived strength.

THE CHALLENGERS

As for the opposition itself, it has improved.

There are two candidates who could campaign well against Rousseff. Aecio Neves, a senator from the vote-rich state of Minas Gerais, is the likely candidate from the PSDB party, which ran Brazil from 1995 to 2003. Pernambuco state governor Eduardo Campos, if he runs, could take supporters from Rousseff's main power base in the relatively poor northeast.

Both Neves and Campos are telegenic figures who could market themselves as left-of-center enough to continue popular welfare programs, but more business-friendly than Rousseff. Either one could attract campaign funds from companies that will be eager for a change if the economy is still flat next year.

A third candidate, environmentalist Marina Silva, appears unlikely to gain massive popular or financial backing but could peel away enough votes from Rousseff to force an uncomfortable run-off, as she did in the 2010 election.

A Datafolha poll published on March 22 showed Rousseff destroying her potential rivals, taking 58 percent of voting intentions compared to 16 percent for Silva, 10 percent for Neves and 6 percent for Campos.

But a chapter from Rousseff's own past shows that early polls don't count for much in Brazil, where few people pay attention until right before the vote.

Eighteen months before she was elected, Rousseff trailed her rival by a whopping 30 percentage points - proving once again that in Brazilian politics, almost anything is possible.

(Editing by Kieran Murray and Claudia Parsons)

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